Oliver Cromwell's House on St Mary's Street is a well-preserved half-timbered building where England's future Lord Protector lived for about a decade before the Civil War. It's now a museum and tourist information centre, with period-furnished rooms depicting domestic life in the 1640s and an exhibition on Cromwell's life and the Civil War.
The house is informative without being overwhelming — it takes about an hour to go round. The location immediately next to St Mary's Church makes for a pleasant short walk from the cathedral close. The staff are knowledgeable and the exhibition strikes a reasonable balance about Cromwell's controversial legacy — neither hagiography nor condemnation.